Influence of Polymer Extensibility on the Temporal Stability Analysis of Planar Jet Flow in FENE-P Fluids

This study extends the linear temporal stability analysis of incompressible, laminar, planar two-dimensional jet flows to viscoelastic fluids described by the FENE-P constitutive equation, extending beyond prior work restricted to the Oldroyd-B limit. The base flow is assumed steady and parallel, and the effects of the Reynolds number (Re), the Weissenberg number (Wi), the solvent viscosity ratio β_n, and the maximum polymer extensibility L are assessed in terms of the growth rates of infinitesimal perturbations and the extent of unstable wavenumber regions, for both sinuous and varicose modes. Components of the conformation tensor A are obtained analytically for the Oldroyd-B limit and numerically for the full FENE-P model. Results show that inertia is destabilizing: increasing Re broadens the unstable region and raises peak temporal growth rates. Viscoelastic effects are generally stabilizing: higher Wi and larger L reduce both the unstable wavenumber range and maximum growth rates; however, this stabilizing influence of Wi is considerably weakened at low extensibility (L = 10), revealing a non-trivial interaction between polymer stretching and relaxation dynamics that is absent in the Oldroyd-B model.